Eichler-Selberg Type Identities for Mixed Mock Modular Forms

Abstract

Using holomorphic projection, we work out a parametrization for all relations of products (resp. Rankin-Cohen brackets) of weight $\frac{3}{2}$ mock modular forms with holomorphic shadow and weight $\frac{1}{2}$ modular forms in the spirit of the Kronecker-Hurwitz class number relations. In particular we obtain new proofs for several class number relations among which some are classical, others are relatively new. We also obtain similar results for the mock theta functions.

28 pages, [v2] some typos corrected, some calculations shortened

References in corpus (4)

• Mock Theta Functions
• Lectures on Quantum Black Holes
• Elliptic curves, modular forms, and sums of Hurwitz class numbers
• Special values of shifted convolution Dirichlet series

Cited by in corpus (8)

• A proof of the Thompson Moonshine Conjecture
• Proof of the Umbral Moonshine Conjecture
• Vector-valued Hirzebruch-Zagier series and class number sums
• Polar harmonic Maaß forms and holomorphic projection
• Theta lifts for Lorentzian lattices and coefficients of mock theta functions
• Quasimodular moonshine and arithmetic connections
• Optimal estimates for an average of Hurwitz class numbers
• Local Maaß forms and Eichler--Selberg type relations for negative weight vector-valued mock modular forms